openai/math

The openai/math repository hosts 719 mathematical manuscripts organized into 372 thematic families, produced by an internal OpenAI model as part of model development evaluations. When existing mathematical benchmarks saturated, OpenAI expanded evaluations to open research problems, posing approximately 4,000 problems to the model, each consuming roughly three hours of ChatGPT Pro thinking compute. Results span diverse mathematical disciplines and include principal findings, companion arguments, alternative proofs, and consequences. Approximately 42% of top-line results have been formally verified using Lean, with ongoing formalization efforts. Notable results include work on the irrationality exponent of π, the Mahler conjecture, Kaplansky's direct-finiteness conjecture, the Mézard–Parisi formula, isomorphism of free group factors, the Hodge Conjecture for CM abelian varieties, and a zero-free region for the Riemann zeta function. Reasoning traces for selected results are publicly released. The repository is notable for demonstrating frontier AI capability on unsolved or hard mathematical research problems, representing a significant and trending milestone in AI-assisted mathematics.